2016/07/14 by Andrew Dancer, Andrew Swann, Dancer, Andrew +1 · 1 citation
Mathematics · #53C26 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1607.04078
openalex publication_date 2016/07/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We discuss various aspects of moment map geometry in symplectic and hyperKähler geometry. In particular, we classify complete hyperKähler manifolds of dimension 4n with a tri-Hamiltonian action of a torus of dimension n, without any assumption on the finiteness of the Betti numbers. As a result we find that the hyperKähler moment in these cases has connected fibres, a property that is true for symplectic moment maps, and is surjective. New examples of hypertoric manifolds of infinite topological type are produced. We provide examples of non-Abelian tri-Hamiltonian group actions of connected groups on complete hyperKähler manifolds such that the hyperKähler moment map is not surjective and has some fibres that are not connected. We also discuss relationships to symplectic cuts, hyperKähler modifications and implosion constructions.